1,920 research outputs found
Renormalization group analysis of the small-world network model
We study the small-world network model, which mimics the transition between
regular-lattice and random-lattice behavior in social networks of increasing
size. We contend that the model displays a normal continuous phase transition
with a divergent correlation length as the degree of randomness tends to zero.
We propose a real-space renormalization group transformation for the model and
demonstrate that the transformation is exact in the limit of large system size.
We use this result to calculate the exact value of the single critical exponent
for the system, and to derive the scaling form for the average number of
"degrees of separation" between two nodes on the network as a function of the
three independent variables. We confirm our results by extensive numerical
simulation.Comment: 4 pages including 3 postscript figure
Statistical and Dynamical Study of Disease Propagation in a Small World Network
We study numerically statistical properties and dynamical disease propagation
using a percolation model on a one dimensional small world network. The
parameters chosen correspond to a realistic network of school age children. We
found that percolation threshold decreases as a power law as the short cut
fluctuations increase. We found also the number of infected sites grows
exponentially with time and its rate depends logarithmically on the density of
susceptibles. This behavior provides an interesting way to estimate the
serology for a given population from the measurement of the disease growing
rate during an epidemic phase. We have also examined the case in which the
infection probability of nearest neighbors is different from that of short
cuts. We found a double diffusion behavior with a slower diffusion between the
characteristic times.Comment: 12 pages LaTex, 10 eps figures, Phys.Rev.E Vol. 64, 056115 (2001
Why social networks are different from other types of networks
We argue that social networks differ from most other types of networks,
including technological and biological networks, in two important ways. First,
they have non-trivial clustering or network transitivity, and second, they show
positive correlations, also called assortative mixing, between the degrees of
adjacent vertices. Social networks are often divided into groups or
communities, and it has recently been suggested that this division could
account for the observed clustering. We demonstrate that group structure in
networks can also account for degree correlations. We show using a simple model
that we should expect assortative mixing in such networks whenever there is
variation in the sizes of the groups and that the predicted level of
assortative mixing compares well with that observed in real-world networks.Comment: 9 pages, 2 figure
Properties of highly clustered networks
We propose and solve exactly a model of a network that has both a tunable
degree distribution and a tunable clustering coefficient. Among other things,
our results indicate that increased clustering leads to a decrease in the size
of the giant component of the network. We also study SIR-type epidemic
processes within the model and find that clustering decreases the size of
epidemics, but also decreases the epidemic threshold, making it easier for
diseases to spread. In addition, clustering causes epidemics to saturate
sooner, meaning that they infect a near-maximal fraction of the network for
quite low transmission rates.Comment: 7 pages, 2 figures, 1 tabl
Epidemics and percolation in small-world networks
We study some simple models of disease transmission on small-world networks,
in which either the probability of infection by a disease or the probability of
its transmission is varied, or both. The resulting models display epidemic
behavior when the infection or transmission probability rises above the
threshold for site or bond percolation on the network, and we give exact
solutions for the position of this threshold in a variety of cases. We confirm
our analytic results by numerical simulation.Comment: 6 pages, including 3 postscript figure
Percolation and epidemics in a two-dimensional small world
Percolation on two-dimensional small-world networks has been proposed as a
model for the spread of plant diseases. In this paper we give an analytic
solution of this model using a combination of generating function methods and
high-order series expansion. Our solution gives accurate predictions for
quantities such as the position of the percolation threshold and the typical
size of disease outbreaks as a function of the density of "shortcuts" in the
small-world network. Our results agree with scaling hypotheses and numerical
simulations for the same model.Comment: 7 pages, 3 figures, 2 table
Edge overload breakdown in evolving networks
We investigate growing networks based on Barabasi and Albert's algorithm for
generating scale-free networks, but with edges sensitive to overload breakdown.
the load is defined through edge betweenness centrality. We focus on the
situation where the average number of connections per vertex is, as the number
of vertices, linearly increasing in time. After an initial stage of growth, the
network undergoes avalanching breakdowns to a fragmented state from which it
never recovers. This breakdown is much less violent if the growth is by random
rather than preferential attachment (as defines the Barabasi and Albert model).
We briefly discuss the case where the average number of connections per vertex
is constant. In this case no breakdown avalanches occur. Implications to the
growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.
Social games in a social network
We study an evolutionary version of the Prisoner's Dilemma game, played by
agents placed in a small-world network. Agents are able to change their
strategy, imitating that of the most successful neighbor. We observe that
different topologies, ranging from regular lattices to random graphs, produce a
variety of emergent behaviors. This is a contribution towards the study of
social phenomena and transitions governed by the topology of the community
NN<sup>k</sup> networks for Content-Based Image Retrieval
This paper describes a novel interaction technique to support content-based image search in large image collections. The idea is to represent each image as a vertex in a directed graph. Given a set of image features, an arc is established between two images if there exists at least one combination of features for which one image is retrieved as the nearest neighbour of the other. Each arc is weighted by the proportion of feature combinations for which the nearest neighbour relationship holds. By thus integrating the retrieval results over all possible feature combinations, the resulting network helps expose the semantic richness of images and thus provides an elegant solution to the problem of feature weighting in content-based image retrieval.We give details of the method used for network generation and describe the ways a user can interact with the structure. We also provide an analysis of the network’s topology and provide quantitative evidence for the usefulness of the technique
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